Table 2 summarizes the phenomena to be explained by any theory of dwarf galaxy evolution. Next to each phenomenon or correlation, we put a score (1-5), indicating our judgement of how secure the observations are. A five indicates that the phenomenon is highly significant statistically and is not due to selection effects; 3 indicates that it may be the result of observational selection, or is only marginally outside the observational uncertainties; smaller numbers indicate that the reported phenomenon is probably not real.
| Phenomenon | Score | Environment |
| Surface-brightness-luminosity relation
(<µ>e  0.75 MB + 35.3)
| 5 | Clusters |
| Surface brightness profile changes with L | 5 | Clusters |
| Metallicity-luminosity relation | 5 | Local group |
| (<[Fe/H]>
-0.2MV - 3.9)
| 3 | Clusters |
| Widespread existence of intermediate age stars | 5 | Local group |
| 3 | Clusters | |
| High M/L in some dE's, | 4 | Local group |
| Moderate M/L in others | 5 | Local group |
| M/L vs. L relation | 4 | Local group |
| (log(M/L)
0.2MV + 3.6)
| ||
| Apparent M/L vs. environment relations | 3 | Local group |
| Velocity anisotropy | 4 | Local group, clusters |
Luminosity Function slope 
-1.3
| 4 | Clusters, groups |
| Richness dependence of dwarf/giant ratio | 4 | Clusters, groups, fields |
| (log d / g 0.65
log g - 1.05
for early-type galaxies with MB < -13) | ||
| Correlation of nucleation with luminosity | 5 | Clusters |
| (N(dE, N) / N(dE)
-0.15MB - 1.7
for dE's in the range -12 > MB > -18) | ||
| Environmental variation of nucleated dE fraction | 5 | Clusters |
| Correlation of nucleation with color | 2 | Clusters |
| Anisotropic spatial distribution around giants | 4 | Local group |
| 3 | Field companions | |
While no theory yet claims to account for all the observed phenomena, the most appealing are those that start from gaseous conditions in the early universe and follow the collapse and cooling of structures within the gravitational hierarchy. Such models (White and Rees 1978; White and Frenk 1991; Cole 1991; Blanchard et al. 1992; Cole et al. 1994; Kauffmann et al. 1994; Lacey and Silk 1991; Lacey et al. 1993) predict the statistical properties of dE galaxies, and may therefore be tested against the global phenomena shown in Table 2. Other models deal with the physical mechanisms of how dE's might have lost their gas (Faber and Lin 1983; Kormendy 1986) how star formation might be regulated (Gerola et al. 1980; Lin and Murray 1992; Silk et al. 1987; Efstathiou 1992), and how at least some dwarfs may have emerged as distinct entities (Gerola et al. 1983; Mirabel et al. 1992). However, such ideas must still be incorporated into a larger theory in order to explain the distribution functions of luminosity, surface brightness, color, nucleation, etc.
Rather than review the models individually, we outline below the physical processes that appear to be important. These are the gravitational collapse of the protogalaxy (Sect. 7.1), cooling of the entrained gas (Sect. 7.3), various external agents that could suppress or slow down the cooling process (Sect. 7.4), various internal agents such as winds or photoionization that could regulate star formation (Sect. 7.5), and finally, environmental influences acting at relatively recent epochs that could convert low-luminosity star forming galaxies into dE's (Sect. 7.6).